The Odds of That

Published: August 11, 2002

(Page 2 of 9)

The same goes for the way we think of miraculous intervention. We need to be told that those lucky last-minute stops for an Egg McMuffin at McDonald's or to pick up a watch at the repair shop or to vote in the mayoral primary -- stops that saved lives of people who would otherwise have been in the towers when the first plane hit -- certainly looked like miracles but could have been predicted by statistics. So, too, can the most breathtaking of happenings -- like the sparrow that happened to appear at one memorial service just as a teenage boy, at the lectern eulogizing his mom, said the word ''mother.'' The tiny bird lighted on the boy's head; then he took it in his hand and set it free.

Something like that has to be more than coincidence, we protest. What are the odds? The mathematician will answer that even in the most unbelievable situations, the odds are actually very good. The law of large numbers says that with a large enough denominator -- in other words, in a big wide world -- stuff will happen, even very weird stuff. ''The really unusual day would be one where nothing unusual happens,'' explains Persi Diaconis, a Stanford statistician who has spent his career collecting and studying examples of coincidence. Given that there are 280 million people in the United States, he says, ''280 times a day, a one-in-a-million shot is going to occur.''

Throw your best story at him -- the one about running into your childhood playmate on a street corner in Azerbaijan or marrying a woman who has a birthmark shaped like a shooting star that is a perfect match for your own or dreaming that your great-aunt Lucy would break her collarbone hours before she actually does -- and he will nod politely and answer that such things happen all the time. In fact, he and his colleagues also warn me that although I pulled all examples in the prior sentence from thin air, I will probably get letters from readers saying one of those things actually happened to them.

And what of the deaths of nearly a dozen scientists? Is it really possible that they all just happened to die, most in such peculiar, jarring ways, within so short a time? ''We can never say for a fact that something isn't a conspiracy,'' says Bradley Efron, a professor of statistics at Stanford. ''We can just point out the odds that it isn't.''

I first found myself wondering about coincidence last spring when I read a small news item out of the tiny Finnish town of Raahe, which is 370 miles north of Helsinki. On the morning of March 5, two elderly twin brothers were riding their bicycles, as was their habit, completing their separate errands. At 9:30, one brother was struck by a truck along coastal Highway 8 and killed instantly. About two hours later and one mile down the same highway, the other brother was struck by a second truck and killed.

''It was hard to believe this could happen just by chance,'' says Marko Salo, the senior constable who investigated both deaths for the Raahe Police Department. Instead, the department looked for a cause, thinking initially that the second death was really a suicide.

''Almost all Raahe thought he did it knowing that his brother was dead,'' Salo says of the second brother's death. ''They thought he tried on purpose. That would have explained things.'' But the investigation showed that the older brother was off cheerfully getting his hair cut just before his own death.

The family could not immediately accept that this was random coincidence, either. ''It was their destiny,'' offers their nephew, who spoke with me on behalf of the family. It is his opinion that his uncles shared a psychic bond throughout their lives. When one brother became ill, the other one fell ill shortly thereafter. When one reached to scratch his nose, the other would often do the same. Several years ago, one brother was hit and injured by a car (also while biking), and the other one developed pain in the same leg.

The men's sister had still another theory entirely. ''She worried that it was a plot to kill both of them,'' the nephew says, describing his aunt's concerns that terrorists might have made their way to Raahe. ''She was angry. She wanted to blame someone. So she said the chances of this happening by accident are impossible.''

Not true, the statisticians say. But before we can see the likelihood for what it is, we have to eliminate the distracting details. We are far too taken, Efron says, with superfluous facts and findings that have no bearing on the statistics of coincidence. After our initial surprise, Efron says that the real yardstick for measuring probability is ''How surprised should we be?'' How surprising is it, to use this example, that two 70-year-old men in the same town should die within two hours of each other? Certainly not common, but not unimaginable. But the fact that they were brothers would seem to make the odds more astronomical. This, however, is a superfluous fact. What is significant in their case is that two older men were riding bicycles along a busy highway in a snowstorm, which greatly increases the probability that they would be hit by trucks.